The lesson for diagnosing a bubble

"Prices have reached what looks like a permanently high plateau." That was Professor Irving Fisher in 1929, prominently reported barely a week before the most brutal stock market crash of the 20th century. He was a rich man and the greatest economist of the age. The great crash destroyed both his finances and his reputation.

"Those who sound the alarm of an approaching... crisis have somewhat exaggerated the danger." That was a renowned commentator, who shall remain nameless for now.

"We are currently showing signs of entering the blow-off or melt-up phase of this very long bull market." That was investor Jeremy Grantham last week.

The normally bearish Mr Grantham mused that while shares seem expensive, historical precedents make it plausible that the S&P 500 will soar from present levels of around 2,700 to more than 3,500 before the crash occurs.

Mr Grantham's speculation is striking because he has tended to be a savvy bubble watcher in the past. But as any toddler can attest, it is not an easy thing to catch one before it bursts.

There are two obvious ways to diagnose a bubble.

One is to look at the fundamentals: If the price of an asset is unmoored from the cash flow it is likely to generate, that is a........